Question

化簡(jiǎn)求值：(

x+2

x2-2x

-

x-1

x2-4x+4

)÷

x-4

x

，且x=3-

2

．

Answer 1

分析：把括號(hào)內(nèi)的分式分母進(jìn)行因式分解并通分計(jì)算，然后把分式的除法運(yùn)算轉(zhuǎn)化為乘法運(yùn)算，約分后把x的值代入計(jì)算即可得解．

解答：解：（

x+2

x2-2x

-

x-1

x2-4x+4

）÷

x-4

x

=[

x+2

x(x-2)

-

x-1

(x-2)2

]÷

x-4

x

=

(x+2)(x-2)-x(x-1)

x(x-2)2

×

x

x-4

=

x-4

x(x-2)2

×

x

x-4

=

1

(x-2)2

，
當(dāng)x=3-

2

時(shí)，
原式=

1

(3 - 2 -2)2

=

1

(1- 2 )2

=

1

3- 2

=

3+ 2

(3- 2 )(3+ 2 )

=

3+ 2

7

．

點(diǎn)評(píng)：本題考查了分式的化簡(jiǎn)求值，解答此題的關(guān)鍵是把分式化到最簡(jiǎn)，然后代值計(jì)算．